The non-Archimedean Green--Griffiths--Lang--Vojta conjecture for commutative algebraic groups with unipotent rank 1

Jackson S. Morrow; Paul Vojta

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arXiv · 2502.10379

The non-Archimedean Green--Griffiths--Lang--Vojta conjecture for commutative algebraic groups with unipotent rank 1

Jackson S. Morrow·Paul Vojta

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Abstract

Let $k$ be algebraically closed field of characteristic zero, let $G$ be a commutative algebraic group over $k$ such that the linear part of $G$ is isomorphic to $\mathbb{G}_a$, and let $X$ be a closed subvariety of $G$. We show that the Kawamata locus of $X$ is equal to a Lang-like exceptional locus of $X$, and furthermore, we identify a condition on $X$ that implies that these loci are proper subschemes of $X$. We also prove the strong form of the non-Archimedean Green--Griffiths--Lang--Vojta conjecture for closed subvarieties of commutative algebraic groups where the linear part is isomorphic to $\mathbb{G}_a \times \mathbb{G}_m^t$.

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BibTeX RIS

Jackson S. Morrow, Paul Vojta. 2025-02-14. The non-Archimedean Green--Griffiths--Lang--Vojta conjecture for commutative algebraic groups with unipotent rank 1. https://arxiv.org/abs/2502.10379

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